A068494 a(n) = n mod phi(n).

0, 0, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 2, 7, 0, 1, 0, 1, 4, 9, 2, 1, 0, 5, 2, 9, 4, 1, 6, 1, 0, 13, 2, 11, 0, 1, 2, 15, 8, 1, 6, 1, 4, 21, 2, 1, 0, 7, 10, 19, 4, 1, 0, 15, 8, 21, 2, 1, 12, 1, 2, 27, 0, 17, 6, 1, 4, 25, 22, 1, 0, 1, 2, 35, 4, 17, 6, 1, 16, 27, 2, 1, 12, 21, 2, 31, 8, 1, 18, 19, 4

Offset

1,9

Comments

By Lehmer's Conjecture, when n > 2 then a(n) = 1 if and only if n is prime. The Notices article states "Lehmer's Conjecture (1932). phi(n) | (n-1) if and only if n is prime." - Michael Somos, Oct 14 2011

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

D. H. Bailey and J. M. Borwein, Exploratory Experimentation and Computation, Notices of A. M. S. 58 (2011) 1410-1419, see p. 1416.

Formula

b^(n - a(n)) == 1 (mod n) for every b coprime to n. - Thomas Ordowski, Jun 30 2017

Mathematica

Table[Mod[n, EulerPhi[n]], {n, 100}] (* Alonso del Arte, Feb 15 2013 *)

Prog

(PARI) for(n=1, 150, print1(n%eulerphi(n), ", "))
(PARI) {a(n) = n % eulerphi(n)}; /* Michael Somos, Oct 14 2011 */
(Haskell)
a068494 n = mod n $ a000010 n  -- Reinhard Zumkeller, Oct 14 2011
(Magma) [n mod EulerPhi(n): n in [1..100]]; // Vincenzo Librandi, Jul 19 2015

Crossrefs

Positions of particular numbers: 0: A007694, 1 (conjectured): A065091, 3: A350777\{1, 2, 3}.

Cf. A055516.

Sequence in context: A023445 A291760 A291759 * A200726 A195040 A250486

Adjacent sequences: A068491 A068492 A068493 * A068495 A068496 A068497

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 11 2002

Status

approved